Method of controlling a wind power plant

ABSTRACT

A method of controlling a wind power plant including an energy storage device, the wind power plant being connected to a power grid and comprising one or more wind turbine generators that produce electrical power for delivery to the power grid, the method comprising: processing grid data related to the power grid to determine a probability forecast for a future state of the grid; and controlling charging and discharging of the energy storage device in accordance with the probability forecast.

TECHNICAL FIELD

The invention relates to a method and control system for controlling awind power plant that includes an energy storage device, and inparticular the invention relates to control of a state of charge of theenergy storage device.

BACKGROUND TO THE INVENTION

A wind power plant comprises a group of wind turbine generators thatconvert energy contained in wind into electrical power, which istypically delivered to a power grid. Differences in wind conditionsacross the site of a wind power plant may entail a different poweroutput from each generator. Moreover, the changeable nature of wind overtime leads to a correspondingly stochastic electrical power output fromeach of the generators.

At the same time, a range of events may occur on the grid that after thepower demanded from the wind power plant, including: changes in powerconsumption by loads connected to the grid; planned changes to the grid,such as adding new loads; real-time electricity price fluctuations; andcritical grid events, including faults such as sudden changes in voltageor frequency on the grid.

The properties of the signal that the wind power plant delivers to thegrid, in particular the frequency and phase angle of that signal, mustbe aligned to instantaneous grid requirements. The wind power plant mustalso deliver active and reactive power at levels demanded by the grid.These requirements can change abruptly during a grid event, in whichcase the wind power plant may have to react by modifying its output.

So, the manner in which the outputs from each wind turbine generator ofthe wind power plant are collated and delivered to the grid must becarefully managed. Accordingly, a wind power plant must incorporatemeans for controlling its output in a dynamic manner to react to varyinggrid demand whilst also compensating for varying wind conditions.

One such means is the inclusion of one or more energy storage deviceswithin the wind power plant. Indeed, including energy storage in someform may be essential if the grid requires the wind power plant to becontrolled as a virtual synchronous machine (VSM) to provide a desiredoutput that is shielded from fluctuations in the generated power, or‘virtual inertia’. Such energy storage devices are typically chargeableand dischargeable on command, and are capable of storing significantquantities of charge that enable them to augment the power supplied bythe wind turbine generators over short but sustained periods.Accordingly, these energy storage devices are distinct from therelatively smaller smoothing capacitors and inductors that are routinelyincluded in power converters and filters of a wind power plant.

In practical terms, a respective energy storage device can be integratedinto each wind turbine generator to provide inertia for the generatorsindividually. For example, an energy storage device may be coupled to aDC link of a power converter of a wind turbine generator. In this case,the energy storage device can be charged or discharged to relievedemands on the wind turbine generator. For example, in a high windscenario the energy storage device could be discharged to allow thegenerator to lower its power output to implement damping, for reducedstructural loading. However, the ability of the energy storage device toact in this way is curtailed by the need to reserve charge that may beneeded during critical grid events.

Alternatively, or in addition, an energy storage device can be attachedto a point of common coupling (PCC) to provide virtual inertia for thepower plant as a whole, in which case similar operational constraintsapply.

In either case, control of the energy storage device for optimisedoperation is a challenge in view of the conflicting demands that arisein service. For example, the need to ensure adequate capacity to absorbspikes in power production must be balanced against the constraint toreserve sufficient charge to compensate for momentary drops in powerproduction or to cope with fault scenarios such as a low voltageride-through. Another factor to consider is that it may be desirable toincrease the state of charge of the energy storage device whenelectricity prices are low, in the hope of increasing revenue by sellingthe energy when prices rise. Conversely, a lower state of charge mightbe expected when electricity prices are high.

It is against this background that the invention has been devised.

SUMMARY OF THE INVENTION

An aspect of the invention provides a method of controlling a wind powerplant. The wind power plant is connected to a power grid, and includesan energy storage device and one or more wind turbine generators thatproduce electrical power for delivery to the power grid. The methodcomprises processing grid data related to the power grid to determine aprobability forecast for a future state of the grid, and controllingcharging and discharging of the energy storage device in accordance withthe probability forecast.

In contrast with known approaches that seek to predict future inputs toa wind power plant in a discrete or deterministic manner, the method ofthe invention bases control of an energy storage device of the windpower plant on a probability forecast for an input to theplant—specifically the state of the grid—which represents potentialfuture grid events probabilistically. In other words, the probabilityforecast for the state of the grid provides an indication of therelative probabilities of a range of events or changes in stateoccurring over a certain time window. This approach is less susceptibleto inaccuracy than a discrete prediction, and thus enables enhancedoptimisation of operation of the energy storage device, which typicallyentails finding an optimal state of charge for the device.

The method may comprise determining a set of chance-constraints relatingto operation of the wind power plant, determining respective limits foreach chance-constraint of the set, and determining, based on eachchance-constraint limit and the probability forecast, a set of deviceconstraints relating to charging and/or discharging of the energystorage device. Charging and discharging of the energy storage device isthen controlled to avoid violating the device constraints, which it isnoted are determined in accordance with the probability forecast.Accordingly, such methods enable optimised usage of the energy storagedevice whilst controlling the risk of violating operational constraintsfor the device and/or the wind power plant, thereby enhancingflexibility in control relative to a conventional approach.

Such methods may also comprise solving an optimisation problem forcontrolling charging and discharging of the energy storage device, theoptimisation problem comprising the device constraints, in which casecharging and discharging of the energy storage device is controlledbased on a control output of the optimisation problem.

The optimisation problem may be solved using a predictive algorithm. Forexample, the method may comprise simulating operation of the wind powerplant using the predictive algorithm. In such embodiments, thepredictive algorithm may be based on a chance-constrained modelpredictive control strategy. In other words, in such embodiments thestate of charge of the energy storage device may be optimised usingchance-constrained model predictive control.

Each limit may define a proportion of operation time of the wind powerplant for which the respective chance-constraint may be violated.

Each chance-constraint of the set of chance-constraints optionallycomprises a requirement to provide any of the following: virtualinertia; grid frequency control; a limited ramp-rate for power deliveredto the power grid; defined power output profiles during a voltageride-through event; power-line flicker reduction; reactive powerinjection; grid oscillation damping; side-side torque damping;drivetrain torque damping; upward yaw control; and noise below athreshold level.

In some embodiments, the method comprises determining a state of chargesetpoint for the energy storage device, and controlling charging anddischarging of the energy storage device in accordance with the state ofcharge setpoint.

The probability forecast optionally comprises any of: a cumulativedistribution function; and a probability density function.

The method may comprise processing data indicative of wind conditions todetermine a probability forecast for wind conditions, and controllingcharging and discharging of the energy storage device in accordance withthe probability forecast for wind conditions. Thus, embodiments of theinvention allow for control of the energy storage device based on thelikelihood of changes to multiple inputs to the wind power plant, namelythe state of the grid and wind conditions. Probability forecasts may bederived for other inputs also, including the states of auxiliary systemsof the wind power plant such as frost protection systems, in which casethese can also be taken into account in the control of the energystorage device.

Charging and discharging of the energy storage device may be controlledin accordance with a prescribed probability of violating one or moregrid requirements.

The grid data may comprise any of the following: data indicative of astate of the power grid; a ramp-rate limit with respect to the powerdelivered to the power grid; a request received from the power grid;grid design data; historical grid data; data indicative of a weak gridobtained from plant-level and/or turbine-level analysis; electricitypricing data; and user-entered forecasts indicative of planned changesto the power grid.

The method may comprise altering operation of one or more wind turbinegenerators of the wind power plant in accordance with the, or eachprobability forecast, and controlling charging and discharging of theenergy storage device in accordance with the altered operation of the oreach wind turbine generator in addition to the, or each, probabilityforecast.

The energy storage device may be electrically coupled to a point ofcommon coupling at which the wind power plant connects to the powergrid. Alternatively, the energy storage device may be integrated into awind turbine generator of the wind power plant. It is also possible forthe wind power plant to include multiple energy storage devices, forexample a storage device integrated into the, or each wind turbinegenerator, and a further energy storage device coupled to the point ofcommon coupling.

Another aspect of the invention provides a control system for a windpower plant. The wind power plant is connected to a power grid andincludes an energy storage device and one or more wind turbinegenerators that produce electrical power for delivery to the power grid.The control system comprises: an input configured to receive grid datarelated to the power grid; a processing module configured to process thegrid data to determine a probability forecast for a future state of thegrid, and generate a control signal arranged to control charging anddischarging of the energy storage device in accordance with theprobability forecast; and an output configured to output the controlsignal.

The control system may be configured to perform the method of the aboveaspect.

The invention also extends to a wind power plant comprising the controlsystem of the above aspect.

It will be appreciated that preferred and/or optional features of eachaspect of the invention may be incorporated alone or in appropriatecombination in the other aspects of the invention also.

BRIEF DESCRIPTION OF THE DRAWINGS

So that it may be more fully understood, the invention will now bedescribed, by way of example only, with reference to the followingdrawings, in which:

FIG. 1 is a schematic diagram of a wind turbine generator that issuitable for use with embodiments of the invention;

FIG. 2 is a schematic diagram of a wind power plant comprising aplurality of wind turbine generators such as that illustrated in FIG. 1;

FIG. 3 is a schematic diagram of an architecture of a full-scaleconverter based wind power plant that is suitable for use withembodiments of the invention;

FIG. 4 is a graph showing time plots of a control input and a powerplant output; and

FIG. 5 is a flow diagram showing a process for controlling the windpower plant of FIG. 3.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

In general terms, embodiments of the invention provide methods andcontrol systems for optimising operation of one or more energy storagedevices incorporated into a wind power plant, by modelling inputs to thewind power plant probabilistically and, based on the respectivelikelihoods of various possible changes in the inputs, determining anoptimal strategy for charging and discharging the, or each, device.

For example, statistical properties or probability forecasts such as aprobability density function may be derived for future wind conditionsand/or grid events, optionally using a predictive algorithm. A setpointfor the state of charge of an energy storage device can then bedetermined in accordance with these probabilistic variables. Thisresults in a setpoint that is less susceptible to inaccuracies in thepredictions and thereby accounts for the stochastic nature of theseinputs to the wind power plant.

Specifically, in the embodiments described below the predictivealgorithm forms part of a chance-constrained model predictive controlapproach, in which limits are set for chance-constraints relating tooperation of the wind power plant, which can then be converted into hardconstraints for operation of one or more energy storage devices of thewind power plant using the probability density function derived for eachinput. These hard constraints then feed into a model predictive controlalgorithm, which solves an optimisation problem to find an optimal stateof charge and/or a charge/discharge strategy for the, or each, energystorage device.

In this context, the relevant chance-constraints relate to changes inthe inputs to the power plant, in particular changes in wind conditionsand grid events, which reflect situations in which either charging ordischarging of the energy storage device(s) may be required, eitherdirectly or indirectly, and this particular form of model predictivecontrol accounts for the chance of each of those situations arising whendetermining a strategy for charging and discharging the energy storagedevice(s).

The conflicting requirements relevant to each chance-constraint can beweighed against one another in the context of the respectiveprobabilities of each of those chance-constraints being violated orhaving to be met in operation, thereby enabling an optimised state ofcharge for the energy storage device(s) to be found.

In a simple example, a pair of conflicting constraints may be arequirement for an energy storage device to provide virtual inertia toabsorb excess power in the event that wind energy peaks momentarily, anda separate requirement for that energy storage device to dischargeenergy during a low voltage ride-through event. The probability thateach of these scenarios will arise can be determined based onprobabilistic modelling of future wind conditions and grid events, andan optimised state of charge can be weighted towards the more likelyscenario, thus minimising the overall likelihood of violating eitherconstraint and ensuring that violations of the chance-constraints arekept within prescribed limits in the long term. In practice, there willbe many more variables and possible outcomes to consider, leading to acomplex optimisation problem to solve.

As electricity prices can vary considerably over short time-frames,there is potential for cost-optimising operation of the energy storagedevice(s) to increase revenue by modifying a charge/discharge strategyfor the energy storage device(s) in accordance with expected pricevariations, while meeting minimum grid requirements in the interim.

Further examples of specific constraints that may be taken into accountare described in more detail below, but it is noted at this stage thatmodelling the various possible scenarios probabilistically enables thesetpoint or other charge/discharge strategy to be optimised to a muchgreater extent than is possible in prior art approaches that deal onlywith instantaneous conditions. Even approaches that attempt to predictfuture inputs in a deterministic manner are vulnerable to inaccuraciesin their predictions, especially for inputs as volatile as windconditions or grid events. In contrast with such approaches, instead ofbasing control on a predicted outcome, embodiments of the invention basecontrol on the respective chances of a range of outcomes.

As any form of forecasting involves uncertainty, previous approaches sethard limits or margins for the state of charge of energy storagedevices, those limits providing a buffer against sub-optimisedoperation. However, implementing such margins precludes full usage ofthe capacity of the device. In this context, an advantage offered byembodiments of the invention is that the optimised state of chargesetpoint for the energy storage device takes into account uncertaintiesin the inputs to the wind power plant and therefore avoids the need toapply margins to the state of charge of the device, thus enhancingutilisation of the capacity of the device.

A specific implementation of such an approach is outlined below withreference to FIGS. 1 to 3, which demonstrates how the inventive conceptcan be incorporated into an existing wind power plant controlarchitecture. It should be appreciated that this implementation isdescribed by way of example only, and embodiments of the invention willfind application in all wind power plant architectures.

Accordingly, to provide context for the invention, FIG. 1 shows anindividual wind turbine generator 1 of a kind that may be controlledaccording to embodiments of the invention. It should be appreciated thatthe wind turbine generator 1 of FIG. 1 is referred to here by way ofexample only, and it would be possible to implement embodiments of theinvention into many different types of wind turbine systems.

The wind turbine generator 1 shown is a three-bladed upwindhorizontal-axis wind turbine (HAWT), which is the most common type ofturbine in use.

The wind turbine generator 1 comprises a turbine rotor 2 having threeblades 3, the rotor 2 being supported at the front of a nacelle 4 in theusual way. It is noted that although three blades is common, differentnumbers of blades may be used in alternative implementations. Thenacelle 4 is in turn mounted at the top of a support tower 5, which issecured to a foundation (not shown) that is embedded in the ground.

The nacelle 4 contains a generator (not shown in FIG. 1) that is drivenby the rotor 2 to produce electrical energy. Thus, the wind turbinegenerator 1 is able to generate electrical power from a flow of windpassing through the swept area of the rotor 2 causing rotation of theblades 3.

FIG. 2 shows the wind turbine generator 1 in the context of a wind powerplant 6 having a plurality of individual wind turbine generators 1;specifically, three wind turbine generators 1 are present in the windpower plant 6 shown in FIG. 2. Each wind turbine generator 1 has anoutput line 7 a that connects to a transmission line 7 b that takeselectrical power generated within the wind power plant 6 to anelectrical grid.

Each wind turbine generator 1 of the wind power plant 6 is connected toa power plant controller (PPC) 8 that controls operation of the windpower plant 6. In this embodiment, the PPC 8 is responsible formonitoring operating conditions and for issuing reactive powerreferences to each wind turbine generator 1 based on an active powerdemand. The PPC 8 therefore represents part of a control system forcontrolling operation of the wind power plant 6.

To this end, the PPC 8 includes an input 9 at which operational data isreceived from each wind turbine generator 1. The input 9 also receivesdata indicative of a state of the grid and data indicative of windconditions. The PPC 8 further includes a processor 10 that, among otherthings, uses the data received at the input 9 to determine active andreactive power references for the wind turbine generators 1.

With reference now to FIG. 3, an example of a wind power plant 12 towhich methods according to embodiments of the invention may be appliedis shown. The example shown in FIG. 3 is based on a full-scale converterarchitecture, although as noted above embodiments of the invention maybe used with other types of converter and in general terms the inventionis suitable for use with all topologies. The wind power plant 12 shownin FIG. 3 may be configured in the same way as the wind power plant 6shown in FIG. 2.

The components of the wind power plant 12 of FIG. 3 are conventional andas such familiar to the skilled reader, and so will only be described inoverview.

The wind power plant 12 shown in FIG. 3 includes a single wind turbinegenerator 1 such as that shown in FIG. 1, but in practice further windturbine generators may be included as shown in FIG. 2.

As already noted, the wind turbine generator 1 comprises an electricalgenerator 20 that is driven by the rotor 2 to produce electrical power.The electrical generator 20 includes a central armature 21 that isdriven by the rotor 2 to rotate within a stator 23. The stator 23contains one or more sets of three-phase windings (not shown) in whichelectrical current is induced in response to varying magnetic fluxcreated by rotation of the armature 21, under the control of a turbinecontroller 27.

The wind power plant 12 also includes a low voltage link 14 defined by abundle of low voltage lines 16 terminating at a coupling transformer 18,which acts as a terminal that connects the wind turbine generator 1 to agrid transmission line that in turn connects to a power grid 19.Electrical power produced by the wind turbine generator 1 is deliveredto the grid 19 through the coupling transformer 18, the power deliveredto the grid 19 being represented as P_(PPC) in FIG. 3.

The electrical generator 20 of a full-scale architecture typicallyproduces multiphase electrical power. In this embodiment, the powerproduced in the electrical generator 20 is three-phase AC, but is not ina form suitable for delivery to the grid 19, in particular because it istypically not at the correct frequency or phase angle. Accordingly, thewind turbine generator 1 includes a power converter 22 and a filter 24disposed between the electrical generator 20 and the couplingtransformer 18, to process the electrical generator output into asuitable waveform having the same frequency as the grid 19 and theappropriate phase angle.

The power converter 22 provides AC to AC conversion by feedingelectrical current through an AC-DC converter, or ‘machine-sideconverter’ 26, followed by a DC-AC converter, or ‘line-side converter’28, in series. The machine-side converter 26 is connected to theline-side converter 28 by a conventional DC link 30, which includes aswitched resistor 32 to act as a dump load to enable excess energy to bedischarged, and a smoothing capacitor 34 providing smoothing for the DCoutput.

Any suitable power converter 22 may be used. In this embodiment, theAC-DC and DC-AC parts of the power converter 22 are defined byrespective bridges of switching devices (not shown), for example in theconfiguration of a conventional two level back-to-back converter.Suitable switching devices for this purpose include integrated gatebipolar transistors (IGBTs) or metal-oxide-semiconductor field-effecttransistors (MOSFETs). The switching devices are typically operatedusing pulse-width modulated drive signals.

The smoothed DC output of the machine-side converter 26 is received as aDC input by the line-side converter 28, which creates a three-phase ACoutput for delivery to the coupling transformer 18.

The AC output of the power converter 22 is carried by the three powerlines 16 that together define the low voltage link 14, each line 16carrying a respective phase. The low voltage link 14 includes the filter24, which in this embodiment comprises a respective inductor 38 with arespective shunted filter capacitor 40 for each of the three power lines16, to provide low-pass filtering for removing switching harmonics fromthe AC waveform.

As noted above, the low voltage link 14 terminates at the couplingtransformer 18 which provides a required step-up in voltage. A highvoltage output from the coupling transformer 18 defines a wind turbinegenerator terminal 42, which acts as a point of common coupling for thewind power plant 12.

As noted above, in a full-scale architecture the line-side converter 28is configured to provide a level of control over the characteristics ofthe AC power produced, for example to increase the relative reactivepower in dependence on grid demand. Noting that the magnitude, angle andfrequency of the output is dictated by grid requirements, and that thevoltage is set at a constant level in accordance with the specificationsof the low voltage link 14, in practice only the current of the ACoutput is controlled, and a converter controller 36 is provided for thispurpose. The converter controller 36 and the turbine controller 27 inturn act on commands received from the PPC 8. In this respect, dashedlines in FIG. 3 represent lines of communication between the PPC 8, theturbine controller 27 and the converter controller 36.

The converter controller 36, the turbine controller 27 and the PPC 8together form part of an overall control system that controls operationof the wind power plant 12.

As noted above, embodiments of the invention relate to control of energystorage devices incorporated into a wind power plant. In this respect,two such devices are shown in FIG. 3: a first energy storage device 44,which is electrically coupled to the DC link 30 of the power converter22 and is operated by the converter controller 36; and a second energystorage device 46, which is electrically coupled to the wind turbinegenerator terminal 42 at the grid side of the power converter 22 and iscontrolled by the PPC 8.

As noted above, although only one wind turbine generator 1 is shown inFIG. 3, in practice a wind power plant typically includes a group ofsuch wind turbine generators, and in such arrangements each wind turbinegenerator may include a respective energy storage device.

Having both the first energy storage device 44 and the second energystorage device 46 maximises the flexibility of the wind power plant 12to respond to different operating scenarios. However, in practice it maybe sufficient to provide energy storage devices in only one of thesepositions, namely either integrated into the or each wind turbinegenerator 1, or coupled to the point of common coupling, i.e. the windturbine generator terminal 42 in this example.

Various other energy storage topologies are also possible. For example,the wind turbine generators of a wind power plant may be assigned to twoor more sub-groups, each sub-group having a respective energy storagedevice.

In principle, various energy storage technologies could be used for thefirst energy storage device 44 or the second energy storage device 46.In practice, batteries and large capacitors are likely options.

The first energy storage device 44 has a state of charge (SoC) 44 a,which is illustrated by a dashed line in FIG. 3. Above this, anotherdashed line represents an upper margin 44 b for the SoC 44 a, which isimplemented to ensure that the device 44 always has reserve capacity toabsorb power if required. Correspondingly, the first energy storagedevice 44 also has a lower margin 44 c for the SoC 44 a, which ensuresthat the device 44 always retains some charge, for example for use ingrid events. For example, the lower margin 44 c may represent 5% charge,and the upper margin 44 b may correspond to 95% charge.

Similarly, the second energy storage device 46 is shown in FIG. 3 withdashed lines representing an SoC 46 a, an upper margin 46 b for the SoC46 a and a lower margin 46 c for the SoC 46 a.

As noted above, by modelling the input uncertainties probabilistically,embodiments of the invention beneficially allow the upper and lowermargins 44, 46 b, 44 c, 46 c to be set to 100% and 0% respectively, ifdesired.

The first energy storage device 44 and the second energy storage device46 are each operable to charge and discharge selectively under thecontrol of the converter controller 36 and the PPC 8 respectively. Inthis embodiment, the converter controller 36 controls the first energystorage device 44 based on commands received from the PPC 8. Thecharging/discharging strategies adopted for each energy storage device44, 46 are determined by the PPC 8 using chance-constrained modelpredictive control to optimise the state of charge of each device 44, 46at all times, as shall be explained in more detail below.

In this embodiment, each of the first and second energy storage devices44, 46 is a DC device. The first energy storage device 44 is connectedto the DC link of the power converter 22, and so can simply connectdirectly. The second energy storage device 46, however, must exchangeelectrical power with the low voltage link 14, which carries three-phaseAC power. Accordingly, an AC/DC converter 48 is provided to act as aninterface between the low voltage link 14 and the second energy storagedevice 46.

The first energy storage device 44 and the second energy storage device46 each have a greatly increased storage capacity relative to either thesmoothing capacitor 34 of the power converter 22 or the filtercapacitors 40. This, combined with the ability for selective chargingand discharging, significantly extends and refines the ability of thewind power plant 12 to match its output to grid requirements. In otherwords, the first and second energy storage devices 44, 46 enhance thevirtual inertia of the wind power plant 12.

The position of the first energy storage device 44 within the powerconverter 22 is also ideal for augmenting operation of the wind turbinegenerator 1, for example to allow power to be consumed within the windturbine generator 1 to reduce structural loads during high loadconditions. Provided it holds sufficient charge, the first energystorage device 44 offers a source of electrical power that can bereadily accessed to supplement the output of the generator 20 ifnecessary, in particular if the output of the generator is deliberatelyreduced to implement side-side torque damping and/or drivetrain torquedamping at high load.

Correspondingly, the second energy storage device 46 is exposed to thecombined output of all of the wind turbine generators 1 of the windpower plant 12, and is therefore ideally placed to smooth and adjustthat output to match grid requirements.

Accordingly, in this embodiment the first energy storage device 44 isprimarily used to assist operation of the wind turbine generator 1 inwhich it resides, and in particular to reduce structural loads arisingin the wind turbine generator 1, whereas the second energy storagedevice 46 is primarily focused on aligning the output of the wind powerplant 12 with grid requirements. However, each energy storage device 44,46 can act to satisfy either role.

It follows from the above that the first energy storage device 44 drawselectrical power from the DC link 30 when in a charging mode and outputselectrical power to the DC link 30 when in a discharging mode.Correspondingly, the second energy storage device 46 draws electricalpower from the low voltage link 14 when in a charging mode, anddispenses electrical power to the low voltage link 14 when in adischarging mode.

FIG. 3 represents the power input to the machine-side converter 26 fromthe generator 20 as P_(ref), while the power output from the line-sideconverter 28 is indicated as P_(gref). The presence of the first energystorage device 44 between the machine-side converter 26 and theline-side converter 28 creates the potential for P_(ref) and P_(gref) todiffer. So, a charge/discharge strategy for the first energy storagedevice 44 may be expressed in terms of target values for P_(ref) andP_(gref).

Correspondingly, charging or discharging the second energy storagedevice 46 impacts the relationship between P_(gref) and P_(PPC), and sothese references may be used to define a charge/discharge strategy forthe second energy storage device 46.

Operating either of the first and second energy storage devices 44, 46in their respective charging modes typically entails drawing on powerproduced by the generator 20 and therefore reducing the electrical powerthat reaches the wind turbine generator terminal 42. In this scenarioP_(ref) exceeds P_(gref), and/or P_(gref) exceeds P_(PPC).

However, each of the first and second energy storage devices 44, 46 arealso able to draw power from the grid 19, beneficially enabling the windpower plant 12 to act as a load. This may be useful in varioussituations, including: recovering power when negative electricity pricesarise due to overproduction; charging the devices to ensure capabilityto perform ancillary functions or to compensate for charge depletion dueto wind events; and to allow frequency down-regulation. In thisscenario, P_(gref) may exceed P_(ref), and P_(PPC) may exceed P_(gref).

With the physical hardware described, the control strategies introducedabove by which the energy storage devices 44, 46 are controlled shallnow be considered in more detail.

As already noted, embodiments of the invention seek to optimise the SoC44 a, 46 a of each of the energy storage devices 44, 46 by taking intoaccount uncertainties in inputs to the wind power plant 12. Theseuncertainties are incorporated by modelling them probabilistically, forexample to produce a probability density function representing aprobability forecast of the input. In parallel, limits are applied tochance-constraints relating to operation of the wind power plant 12.These limits are used in combination with the probability densityfunction for each input to generate hard constraints, or ‘deviceconstraints’, for operation of the first and second energy storagedevices 44, 46 that feed into a model of the wind power plant 12 that isconfigured according to the principles of model predictive control. Inthis respect, while using model predictive control in the context ofoperating a wind power plant is known for other purposes, introducingchance-constraints allows further optimisation, which is especiallyuseful for control of energy storage devices.

The most relevant inputs having significant uncertainty are windconditions—or power production in dependence on wind conditions—and thestate of the grid 19. In this embodiment, control of the first energystorage device 44 prioritises uncertainties associated with windconditions, as load effects of wind changes are local to the firstenergy storage device 44. Correspondingly, control of the second energystorage device 46 prioritises uncertainties associated with the state ofthe grid 19. In other embodiments the reverse may be the case, andtypically each device 44, 46 is controlled to account for alluncertainties for which data is available, at least to some extent.

The main objectives underlying the optimisation are to define values forP_(ref) and P_(gref) that enable the wind power plant 12 to comply withgrid requirements, maximise the produced power P_(PPC) and minimisestructural loading on the or each wind turbine generator 1. Otherobjectives may include reducing the frequency of charge/discharge cyclesfor each energy storage device 44, 46 to minimise wear, and avoidingpenalties for failing to meet grid requirements.

Meeting these objectives amounts to defining a suitable charge/dischargestrategy for each of the first and second energy storage devices 44, 46,and so at the most basic level entails finding an optimal SoC 44 a, 46 afor each device 44, 46 at any given time.

In practice, the outputs of the optimisation process may be controlsignals for effecting charging or discharging of the first and secondenergy storage devices 44, 46, which may be expressed ascharge/discharge commands and/or as target values for P_(ref), P_(gref)and P_(PPC). Control signals may also be generated for adjusting aspectsof the operation of a wind turbine generator 1 that impact operation ofan energy storage device 44, 46. For example, the PPC 8 may generatesetpoint commands to derate or overboost the wind turbine generator 1 toinfluence power production in a complementary manner to thecharge/discharge strategy for the or each energy storage device 44, 46.

As the skilled reader will appreciate, in broad terms a standardoptimisation problem may be expressed as:

$\begin{matrix}\min & {f\left( {x,\xi} \right)} \\{{subject}\mspace{14mu}{to}} & {{g\left( {x,\xi} \right)} = 0} \\\; & {{h\left( {x,\xi} \right)} \geq 0}\end{matrix}$

where ξ is the vector of uncertainty. Under the chance-constrainedmethod, the inequality constraint is formulated as:

P(h(x,ξ)≥0)≥p

where pϵ[0, 1] is the probability density function of fulfilling theconstraint h(x, ξ))≥0. Thus, to minimise f(x, ξ), this approach setslimits on the extent to which the chance-constraints may be violatedwithin a predetermined time period, or ‘window’, which in this caseentails finding an optimal SoC 44 a, 46 a for each of the first andsecond energy storage devices 44, 46.

The relevant window for each constraint may be different, and may befixed in advance, for example if the grid 19 dictates the windowexplicitly or implicitly as part of a constraint. Alternatively, thewindow may be adjusted as part of the control approach. For constraintshaving a finite tail, for example those with an upper limit to theseverity, it may be possible to operate with a zero chance of violatingthe constraint, so that the window is effectively infinite. An exampleof a constraint having a finite tail is power production, which islimited by the electrical characteristics of each wind turbine generator1. While power production by a wind turbine generator 1 depends on windconditions and is therefore uncertain, it cannot exceed the physicallimitations of the wind turbine generator 1.

Although the following description reflects how the chance-constrainedmodel predictive control approach may be used to solve the optimisationproblem in the context of the wind power plant 12 described above, it isnoted that the optimisation problem is solved for each energy storagedevice 44, 46 and can be solved if only one such device is present inthe wind power plant 12. Where multiple energy storage devices arepresent, however, they can be considered collectively within theanalysis. For example, the problem could be formulated so as to find anoptimum collective state of charge across all energy storage devices, sothat the distributed energy storage devices are treated as a unifiedenergy source. This will depend to some extent on where the energystorage devices 44, 46 are positioned within the wind power plant 12,however. For example, while it may be relatively straightforward totreat devices on the line-side as unified, storage devices that areintegrated into power converters may need to be responsive to theindividual needs of their respective wind turbine generators.

In this embodiment, the optimisation problem is solved for each energystorage device 44, 46 by the PPC 8 to determine a charge/dischargestrategy for each device 44, 46. The charge/discharge strategy generatedfor the first energy storage device 44 is then transmitted to theconverter controller 36 to be implemented. The charge/discharge strategyfor the second energy storage device 46 is implemented by the PPC 8directly. In other embodiments, the converter controller 36 mayimplement its own optimisation to determine a charge/discharge strategyfor the first energy storage device 44 independently.

As noted earlier, the PPC 8 has access to data that is indicative ofwind conditions, as well as data indicating the state of the grid 19.

The data that is indicative of wind conditions may include measurementsof instantaneous parameters such as wind speed and direction, turbulenceintensity and shear. The PPC 8 may also have access to data thatenhances its ability to assess how wind conditions may change over apredefined window. For example, the PPC 8 may receive or hold site mapdata, meteorological data and data from Lidar sensors. It is also notedthat present conditions at one location in the wind power plant 12 maybe indicative of future conditions at another point in the power plant12, and so this can also be taken into account.

By analysing such data, the PPC 8 can derive a probability forecast suchas a probability density function indicating relative probabilities forthe occurrence of a range of changes to wind conditions within thedefined window. The changes that may be characterised probabilisticallymay include changes in turbulence intensity and low frequency changes inmean wind speed, as well as the occurrence of more extreme windconditions such as gusts, changes in wind direction and the occurrenceof extreme positive or negative shear. For example, a probabilitydensity function computed by the PPC 8 may indicate, over a window oftwo minutes, probabilities for gusts at different speeds, directionsand/or durations.

For the grid 19, the key uncertainties that need to be predicted tooptimise operation of the first and second energy storage devices 44, 46are the occurrence of critical events. Such events may include a varietyof faults, such as a weak grid scenario arising or sudden changesmanifesting in the grid voltage in terms of its frequency, phase oramplitude, including low voltage and under voltage situations. Othergrid events may include: changes in power consumption by loads connectedto the grid; planned changes to the grid, such as adding new loads;real-time electricity price fluctuations; and ancillary service needsarising, such as inertia emulation, primary/secondary frequency controland fast ramping.

Another uncertainty comes in the form of inter/intra-area oscillation,which relates to the occurrence of resonance—and, in turn, oscillatingpower and voltage—as a result of exciting natural frequencies, oreigenmodes, when the signals of different wind turbine generators arecombined. In this respect, the signals from each generator, ortransmission line, have characteristics that reflect the individualinertia, time constants, delay and capacitance of the generator and/ortransmission line. For example, a pair of independent wind turbinegenerators within the power plant may produce outputs that are slightlyout-of-phase.

To assess the probability of such events occurring within the predefinedtime window, the PPC 8 can process various types of data alongsideindications of the present state of the grid 19 and/or demands receivedfrom the grid 19, such as the design of the grid 19, including knownvulnerabilities, and historical data indicating grid behaviour. Inaddition, plant-level and turbine-level techniques for detecting weakgrids are known, and these can feed into the analysis performed by thePPC 8. Forecasts entered by grid operators based on planned changes tothe grid 19 may also be taken into account.

Similarly to the other inputs that are analysed, the output from thisstage of the analysis is a probability density function indicating thelikelihood of grid events occurring within the predefined window.

Another form of uncertainty that may be taken into account is the needto power ancillary services, such as frost protection systems. Suchsystems can consume a significant level of power internally and so maycause a disturbance to the power output if not taken into account.

Modelling the above inputs to the wind power plant 12 in a probabilisticmanner in the context of optimising the SoC 44 a, 46 a of each energystorage device 44, 46 gives rise to a set of chance-constraints, whichcan be tailored to each application. Limits are applied to thesechance-constraints, each limit defining the proportion of time for whichthe respective chance-constraint may be violated in the long term.

The chance-constraint limits are then converted, using the probabilitydensity functions for the inputs, into hard device constraints foroperation of the energy storage devices 44, 46. These device constraintsthen feed into a chance-constrained model predictive control analysis todetermine optimal values for the SoC 44 a, 46 a of each energy storagedevice 44, 46.

Some examples of chance-constraints that may be used as a precursor forthe chance-constrained model predictive control analysis are set outbelow.

A first chance-constraint may be for the first and/or second energystorage device 44, 46 to have capacity to provide virtual inertia, and atypical limit for this constraint may be that it must be satisfied morethan 99% of the time. This entails the device 44, 46 having an SoC 44 a,46 a at a level between the upper and lower margins 44 b, 46 b, 44 c, 46c so that the device 44, 46 is able to charge and/or dischargeelectrical power as may be necessary to provide inertia, for examplewhen there are fluctuations in the power production of a wind turbinegenerator 1 of the wind power plant 12.

A similar chance-constraint limit would be to ensure that the firstand/or second energy storage device 44, 46 has capacity for gridfrequency control more than 99% of the time, especially where the windpower plant 12 contributes to a primary reserve that enables the grid 19to respond quickly to changes in demand and/or production. Thischance-constraint is therefore responsive to a grid event in which thegrid frequency deviates from a nominal level.

Other chance-constraint limits related to grid events are to ensure thatthe first and/or second energy storage device 44, 46 has capacity forreactive power injection more than 95% of the time, and/or to supplyactive power alongside reactive power when demanded. In this respect,the inclusion of the first and/or second energy storage device 44, 46 isexpected to be particularly useful for alleviating the latter of theseconstraints.

Further chance-constraints related to grid events include ensuringcapacity for grid oscillation damping more than 99% of the time,maintaining the ability to follow specified power output profiles duringlow voltage ride-through/under voltage ride-through events more than 99%of the time, or provision for limiting the ramp rate of the outputP_(PPC) to the grid 19 more than 99% of the time.

Some chance-constraints related to reducing structural loading on a windturbine generator 1 include ensuring the first and/or second energystorage device 44, 46 has capacity to provide side-side torque dampingand/or drivetrain torque damping more than 98% of the time. Anotherchance-constraint related to structural loading is to ensure that formore than 90% of the time the energy storage device 44, 46 has capacityfor upward yaw control/hydraulic pressure for at least five minutes inthe event of a grid error in a context of critical wind speeds. Thesechance-constraints are primarily relevant for the first energy storagedevice 44, which as noted above may be focused on augmenting operationof the wind turbine generator 1 in which it resides for reducedstructural loads, in particular in response to grid events. However, thesecond energy storage device 46 may also be used for this purpose and somay be controlled against these chance-constraints also.

A further relevant chance-constraint is to ensure the first and/orsecond energy storage device 44, 46 has capacity to maintain powervariation at certain frequencies on the power spectrum, or ‘power-lineflicker’, below the regulatory limit more than 99% of time.

A final example of a chance-constraint that may be taken into account isa requirement to limit noise to a prescribed threshold at least 95% ofthe time, which typically entails controlling blade pitch and/or rotorspeed to limit noise under certain wind conditions or at particulartimes.

The above examples demonstrate typical chance-constraints that arise inthe context of optimising the SoC 44 a, 46 of an energy storage device44, 46 within a wind power plant 12, and moreover how thesechance-constraints can be prioritised by adjusting the respective risksof failing to fulfil each of them. So, chance-constraints that arerequired to be satisfied in more than 99% of cases, for example thoserelating to assisting grid recovery, are of higher priority thanchance-constraints that must only be satisfied 95% of the time, such aslimiting noise. This prioritisation can be adjusted for eachapplication, and will typically reflect the consequences of violatingeach constraint.

The risks of failing to meet each chance-constraint relate to thestorage constraints of each energy storage device, to the extent thatfailure to satisfy a chance-constraint typically means that the storagelimits of a device have been reached. For example, a chance-constraintthat requires the energy storage device 44, 46 to discharge power maynot be satisfied if the device 44, 46 is already fully discharged.Conversely, a fully charged device cannot consume power to meet achance-constraint.

It follows from the above that assigning a respective limit to eachchance-constraint may be considered as effectively prescribing alikelihood of meeting grid requirements. This likelihood can thereforebe prescribed explicitly in the optimisation problem, and so can be usedas a design parameter that can be adjusted for each applicationaccording to the requirements imposed on a wind power plant and/or windturbine generator by a power grid. This in turn affords greaterflexibility in how the wind power plant 12 is operated, allowingenhanced optimisation in various respects. In particular, this approachenables the power output of the wind power plant 12 to be maximisedwhilst controlling the extent to which constraints pertaining to gridrequirements are violated.

FIG. 4 illustrates graphically how the optimisation process set outabove improves the performance of the wind power plant 12 in practice.FIG. 4 shows two time-plots: a lower plot 50, which represents a controlinput to the power plant 12; and an upper plot 52, which represents thepower production P_(PPC) of the wind power plant 12. Upper and lowerhorizontal dashed lines in FIG. 4 denote margins within which powerproduction must be held to satisfy grid requirements.

The upper plot 52 comprises a solid line surrounded by a shaded region.The solid line represents a certainty equivalent output from the windpower plant 12, namely the output that would be achieved in the absenceof uncertainties. The shaded region represents the area within which theactual output may deviate due to uncertainties with a probability of99%. In other words, the shaded region represents the potential impactof the chance-constraints in 99% of cases. Accordingly, to fulfil gridrequirements 99% of the time, this shaded region must be kept within thelower and upper margins.

In this example, the shaded region has been calculated by applying aMonte Carlo analysis to the results of a series of simulations of thesystem in which different uncertainties are realised at random.

FIG. 5 is a flow diagram summarising a process 60 for controlling thewind power plant 12, which is performed by the PPC 8 in this example.

The process 60 begins with the PPC 8 processing data relating to one ormore inputs to the wind power plant 12 at step 62, to model the inputuncertainties probabilistically to obtain a probability forecast foreach input to the power plant 12. For example, the probability forecastmay be in the form of a probability density function. The data relatingto inputs to the wind power plant 12 may comprise the data indicative ofa state of the grid 19 and/or data indicative of wind conditions, thisdata being received at the input 9 of the PPC 8. In an embodiment, onlythe state of the grid 19 may be taken into account, in particular ifonly the second energy storage device 46 is present in the wind powerplant 12.

The process 60 continues with the PPC 8 determining, at step 64, limitsfor the relevant chance-constraints governing operation of the windpower plant 12. A chance-constraint relates to satisfying operationalrequirements, and the limit of each chance-constraint is the likelihoodof satisfying the constraint, typically expressed in terms of apercentage of operation time in which the constraint will not beviolated in the long term. For example, a limit for successfullydelivering active power to the grid 19 when demanded may be set at 99%of the time, meaning that it is allowable for the wind power plant 12 tofail to deliver active power demanded by the grid up to 1% of the timein the long term.

Each limit is determined according to operational objectives and gridrequirements, and so differs for each application. Determining achance-constraint limit may entail obtaining it from an internal memory,receiving a limit from an external source such as the grid 19, or a userdefining a constraint limit via an interface to the PPC 8.

The PPC 8 then uses the probability density functions generated for theinputs to the wind power plant 12 to convert, at step 66, thechance-constraint limits identified in the previous step into harddevice constraints for the SoC 44 a, 46 a of each energy storage device44, 46. These device constraints may include upper and lower thresholdsfor the SoC 44 a, 46 a for each device, and maximum charging ordischarging rates, for example.

The device constraints are configured such that if they are adhered toand the energy storage devices 44, 46 are operated within them, eachchance-constraint will not be violated beyond its respective limit. So,referring again to the above example, meeting the device constraints foreach energy storage device 44, 46 will ensure that the wind power plant12 delivers active power to the grid 19 when demanded at least 99% ofthe time in the long term.

The next step of the process 60 is to determine, at step 68, acharge/discharge strategy for each energy storage device 44, 46 based onthe device constraints derived for the SoC 44 a, 46 a of each energystorage device 44, 46. A charge/discharge strategy may take the form ofa respective setpoint for each energy storage device 44, 46, forexample. Alternatively, the charge/discharge strategy may comprise ratesof charging or discharging for each device 44, 46.

The charge/discharge strategy is determined by solving a recedinghorizon optimisation problem over a defined window using a modelpredictive control algorithm, to find an optimal SoC 44 a, 46 a for eachenergy storage device 44, 46.

The optimisation problem takes into account the initial conditions ofthe system, a set of equality constraints, a set of inequalityconstraints, and a cost function. The initial conditions include, forexample, the present wind conditions, grid state and the SoC 44 a, 46 aof each storage device 44, 46. The equality constraints define a systemmodel representing the system dynamics. The inequality constraintsinclude the device constraints derived in step 66 and other operationalconstraints, including the storage capacity of each storage device 44,46. The cost function dictates the form of solution required from theoptimisation problem, and may be configured in various ways. Forexample, the cost function may be arranged to account for differencesbetween power production and power output relative to the inputs to anddemands on the wind power plant 12, and deviances in the SoC 44 a, 46 aof each storage device 44, 46 from desired values. The cost function mayalternatively be configured to ensure the wind power plant 12 operatesin the most cost effective manner, for example by maximising powerproduction whilst minimising structural loading on the wind turbinegenerators 1 and charging cycles for the energy storage devices 44, 46.

Solving the optimisation problem generates a control action relating toa charge/discharge strategy for the energy storage devices 44, 46, whichas noted above may be in the form of respective setpoints for the SoC 44a, 46 a of each device 44, 46.

Finally, the PPC 8 implements the charge/discharge strategy determinedin the previous step and controls, at step 70, charging and dischargingof the energy storage devices 44, 46 in accordance with the output ofthe optimisation problem, for example the setpoint SoC for each energystorage device 44, 46. In a broad sense, therefore, the energy storagedevices 44, 46 are controlled in accordance with the probabilityforecasts for each input, such as the grid state.

It is noted that control of the first energy storage device 44 typicallyentails the PPC 8 issuing a control command to the converter controller36. The second energy storage device 46 is controlled by the PPC 8directly in this embodiment.

The process 60 then reiterates continuously, with the PPC 8 firstupdating the probabilistic models of the input uncertainties and thenupdating the chance-constraints and device constraints accordingly. Thecharge/discharge strategies for each energy storage device 44, 46, forexample the respective setpoint states of charge, are therefore updateddynamically to reflect any changes to the input data, the states ofcharge of the devices 44, 46 and/or the constraints.

The skilled person will appreciate that modifications may be made to thespecific embodiments described above without departing from theinventive concept as defined by the claims.

1. A method of controlling a wind power plant including an energystorage device, the wind power plant being connected to a power grid(19) and comprising one or more wind turbine generators that produceelectrical power for delivery to the power grid, the method comprising:processing grid data related to the power grid to determine aprobability forecast for a future state of the grid; and controllingcharging and discharging of the energy storage device in accordance withthe probability forecast.
 2. The method of claim 1, comprising:determining a set of chance-constraints relating to operation of thewind power plant; determining respective limits for eachchance-constraint of the set; determining, based on eachchance-constraint limit and the probability forecast, a set of deviceconstraints relating to charging and/or discharging of the energystorage device; and controlling charging and discharging of the energystorage device to avoid violating the device constraints.
 3. The methodof claim 2, comprising: solving an optimisation problem for controllingcharging and discharging of the energy storage device, wherein theoptimisation problem comprises the device constraints; and controllingcharging and discharging of the energy storage device based on a controloutput of the optimisation problem.
 4. The method of claim 3, comprisingsolving the optimization problem using a predictive algorithm.
 5. Themethod of claim 4, comprising simulating operation of the wind powerplant using the predictive algorithm.
 6. The method of claim 4, whereinthe predictive algorithm is based on a chance-constrained modelpredictive control strategy.
 7. The method of claim 2, wherein eachlimit defines a proportion of operation time of the wind power plant forwhich the respective chance-constraint may be violated.
 8. The method ofclaim 2, wherein each chance-constraint of the set of chance-constraintscomprises a requirement to provide any of the following: virtualinertia; grid frequency control; a limited ramp-rate for power deliveredto the power grid; defined power output profiles during a voltageride-through event; power-line flicker reduction; reactive powerinjection; grid oscillation damping; side-side torque damping;drivetrain torque damping; upward yaw control; and noise below athreshold level.
 9. The method of claim 1, comprising determining astate of charge setpoint for the energy storage device, and controllingcharging and discharging of the energy storage device in accordance withthe state of charge setpoint.
 10. The method of claim 1, wherein theprobability forecast comprises any of: a cumulative distributionfunction; and a probability density function.
 11. The method of claim 1,comprising processing data indicative of wind conditions to determine aprobability forecast for wind conditions, and controlling charging anddischarging of the energy storage device in accordance with theprobability forecast for wind conditions.
 12. The method of claim 1,comprising controlling charging and discharging of the energy storagedevice in accordance with a prescribed probability of violating one ormore grid requirements.
 13. The method of claim 1, wherein the grid datacomprises any of the following: data indicative of a state of the powergrid; a ramp-rate limit with respect to the power delivered to the powergrid; a request received from the power grid; grid design data;historical grid data; data indicative of a weak grid obtained fromplant-level and/or turbine-level analysis; electricity pricing data; anduser-entered forecasts indicative of planned changes to the power grid.14. The method of claim 1, comprising altering operation of one or morewind turbine generators of the wind power plant in accordance with theor each probability forecast, and controlling charging and dischargingof the energy storage device in accordance with the altered operation ofthe or each wind turbine generator.
 15. The method of claim 1, whereinthe energy storage device is electrically coupled to a point of commoncoupling at which the wind power plant connects to the power grid, or isintegrated into a wind turbine generator of the wind power plant.
 16. Acontrol system for a wind power plant including an energy storagedevice, the wind power plant being connected to a power grid andcomprising one or more wind turbine generators that produce electricalpower for delivery to the power grid, the control system comprising: aninput configured to receive grid data related to the power grid; aprocessing module configured to: process the grid data to determine aprobability forecast for a future state of the grid; and generate acontrol signal arranged to control charging and discharging of theenergy storage device in accordance with the probability forecast; andan output configured to output the control signal.
 17. A wind powerplant comprising the control system of claim
 16. 18. A wind power plantconnected to a power grid, comprising: an energy storage device; atleast one wind turbine, comprising: a tower; a nacelle disposed on thetower; a generator disposed in the nacelle and configured to produceelectrical power for delivery to the power grid; a rotor coupled to thegenerator; and a plurality of blades disposed at a distal end of therotor; and a control system, comprising: an input configured to receivegrid data related to the power grid; a processing module configured to:process the grid data to determine a probability forecast for a futurestate of the grid; and generate a control signal arranged to controlcharging and discharging of the energy storage device in accordance withthe probability forecast; and an output configured to output the controlsignal.
 19. The wind park of claim 18, wherein the processing module isfurther configured to: determine a set of chance-constraints relating tooperation of the wind power plant; determine respective limits for eachchance-constraint of the set; determine, based on each chance-constraintlimit and the probability forecast, a set of device constraints relatingto charging and/or discharging of the energy storage device; and controlcharging and discharging of the energy storage device to avoid violatingthe device constraints.